Am i ever folding here?

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Posted by posted in Low Stakes

Am i ever folding here?

Blinds: $0.02/$0.05 (6 Players) CO: $2.00
BN: $7.54
SB: $5.02 (Hero)
BB: $4.87
UTG: $5.14
MP: $6.00
Villain on the BN is a 25/12 after 50 hands. AF 7.5.
Preflop ($0.07) Hero is SB with K K
2 folds, CO checks, BN calls $0.05, Hero raises to $0.25, BB folds, CO folds, BN calls $0.20
Value raise for me out of position. A 25% range for villain should include a lot of broadways, pocket pairs and medium suited connectors.
Flop ($0.60) 3 4 8
Hero bets $0.17, BN raises to $0.60, Hero calls $0.43
Looks pretty dry to me and I'm betting for value

According to Equilab, villain has a set 1.1% of the time which is my main concern and most of his range will be overcards and backdoor straight draws. His raise is interesting but i think a mandatory call for me.

Maybe i should bet bigger or shove his raise?
Turn ($1.80) 3 4 8 5
Hero checks, BN bets $1.30, Hero calls $1.30
I check here which i would do with 100% of my range out of position and call
River ($4.40) 3 4 8 5 3
Hero checks, BN bets $5.39 and is all in, Hero calls $2.87 and is all in
Board pairs, but i think any 3 is unlikely. The 67 and A2 get there. Really im worried about sets. I don't think aces are likely given his limp call pre flop

Thoughts?
Final Pot BN wins and shows a straight, Four to Eight.
SB lost and shows two pair, Kings and Threes.
BN wins $9.72
Rake is $0.42

If i use Equilab to modify his range after the flop, assuming he only raises draws and top pair or better, I still have 90% equity against his range

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